"Reduction of obesity" is a misleading way of phrasing it, as it is a collection of a number of other factors that increase the chance of obesity. Breast feeding is the baseline.
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Dave ClarkeJul 16 '13 at 17:03

2 Answers
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An important thing which most analyses of breastfeeding studies that I have read note is that women who breastfeed tend to have higher IQs and incomes than women who don't, at least in first world countries. Because of the changes in lifestyle factors which result, it is nearly impossible to sort out what impacts on women and children are from breastfeeding and what are from better access to quality foods, better access to educational resources, and so on. This is even more true of women who breastfeed for an extended period of time.

From the World Health Organization comes a paper on the long-term effects of breastfeeding - in general, with some studies only going to 3 months - dated 2013. The Skeptical OB has a summary. In the case of most health benefits that are commonly claimed to be associated with breastfeeding and even more with extended breastfeeding the WHO determined that confounding variables such as maternal intelligence, education, and income could not be ruled out. These benefits included a slight reduction in obesity, a tiny increase in IQ, and a small decrease in blood pressure. The conclusion is:

Total cholesterol. There was no effect in the overall meta-analyses. In the 2007 review, there was a significant effect among adults, which is no longer present in the updated analyses. The UK trial of preterm infants showed a small protective effect (3), while the Belarus trial did not report on this outcome. We conclude that breastfeeding does not seem to protect against total cholesterol levels.

Blood pressure. The pooled estimate from the high-quality studies indicates a small reduction of less than 1 mmHg in systolic pressure among breastfed subjects, and no significant protection in terms of diastolic pressure. Residual confounding may be an important problem. The Belarus and UK preterm trials found no effect of breastfeeding (2,4). We conclude that the protective effect of breastfeeding, if any, is too small to be of public health significance.

Diabetes. There was substantial protection in the pooled analyses, with a 34% reduction, but few studies are available and their results were considerably heterogeneous. Only two high-quality studies were identified, with conflicting results (one showing an increase and another a reduction among breastfed subjects). The randomized trials did not present any results on these outcomes. Our conclusion is that further studies are needed on this outcome.

Overweight-obesity. In the pooled analyses of all studies, breastfeeding was associated with a 24% reduction in overweight and/or obesity, but the reduction was only 12% in the high-quality studies. Residual confounding may be still affecting these results, because protection is not evident in studies from low and middle-income countries where the social patterning of breastfeeding is not clear cut. The Belarus trial did not find an association (4). We conclude that breastfeeding may provide some protection against overweight or obesity, but residual confounding cannot be ruled out.

Intelligence tests. Breastfeeding was associated with an increase in 3.5 points in normalized test scores in the pooled analyses of all studies, and 2.2 points when only the high-quality studies are included. The two randomized trials also found significant effects (1,5). We conclude that there is strong
evidence of a causal effect of breastfeeding on IQ, although the magnitude of this effect seems to be modest.

The most recent Harvard study referenced in the other answer also has serious flaws as reported by the Skeptical OB. As with other breastfeeding studies, the major flaw is that this study did not take out the confounding variables.

After doing some research I have found two studies which attempted to separate out socio-economic status and educational status in the mother from breastfeeding status. Unfortunately neither measured breastfeeding duration over 2 years and both are based on the same group of children. The studies looked at a less than six month duration and a 12-18 month duration of breastfeeding. Both studies [1] and [2] did show the minor IQ bump, as mentioned above in the quote from the WHO paper.

I am not convinced that all the benefits of breastmilk have been discovered yet, as it seems that something that is newly discovered and amazing about breastmilk is being discovered every year. However so far the scientific evidence does not support a significant public health benefit over the long term to extended breastfeeding.

The initial challenges to breastfeeding tend to be in the early months - getting the milk supply established, getting past cluster feeding and growth spurts, dealing with pain for the mother, the transition to going back to work, and so on. In my opinion overstating the small benefits of breastfeeding in general and extended breastfeeding in particular will not help families who desire to breastfeed be any more motivated to overcome these challenges.

No matter what the studies say, for some families there will be benefits to breastfeeding up to and past age two. There are all sorts of intangibles, many mentioned here that are backed up by experience, not science. Breastfeeding provides cuddle time with notoriously on-the-go toddlers. It may help with hydration during illness. It can be a tool for calm in the emotionally stormy times of toddlerhood. If extended breastfeeding is working, that's great. There's no need to exagerate the health benefits to defend it.

In 2008 the American Academy of Family Physicians said this in their position paper:

It has been estimated that a natural weaning age for humans is between
two and seven years. Family physicians should be knowledgeable
regarding the ongoing benefits to the child of extended breastfeeding,
including continued immune protection, better social adjustment and
having a sustainable food source in times of emergency. The longer
women breastfeed, the greater the decrease in their risk of breast
cancer. There is no evidence that extended breastfeeding is harmful to
mother or child.

Many scientific studies prove the point that longer breastfeeding enhances the
neurodevelopment of infants and their intellectual and scholastic ability in later life. from one of these studies increase in the IQ by breastfeeding is directly related to the duration of breastfeeding. These benefits are strongest for the infants of low birth weight on breastmilk feeding. It is found that Poor who are more likely to
enter into child malnutrition are more likely to benefit from enhanced optimal breastfeeding
practices.

WHO recommends that breastfeeding should continue for two years or more without accurately establishing a maximum duration for breastfeeding.In addition, there is insufficient evidence on the advantages and disadvantages of continuing breastfeeding after two years.

As I linked above, here's an overview of the AAFP's position. It's not as accurate as one might hope. Unfortunately my research indicates that a lot of articles out there on extended breastfeeding seriously overstate the benefits in developed nations.
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justktJul 15 '13 at 16:38

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@Javier Yes, you can post a question and then immediately post an answer. This is usually an indication that someone came across a problem, solved it, and felt that the solution was good enough to share on the site (and that type of scenario is certainly encouraged). If you feel the answer is biased strongly, comments highlighting counter-points or flaws may be appropriate, or even possibly down-voting. There are a lot of very polarizing topics in parenting. Expressing strong opinions about these topics is okay, so long as it doesn't become argumentative or demeaning to those who disagree.
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BeofettJul 16 '13 at 19:13

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After saying that, I have to downvote this answer. While I appreciate the effort put forth, few, if any, of the statements made are supported by the references cited. For example, the claim that " The increase in the IQ by breastfeeding is directly related to the duration of breastfeeding" appears to be based solely upon a study of a small cohort of very small birth weight babies, and the duration of breastfeeding was only measured up to 8+ months, whereas the question is explicitly about breastfeeding past 2 years.
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BeofettJul 16 '13 at 19:23

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In fact, of the links and references presented, all but one are restricted to research on breastfeeding periods of 1 year or less. The only one that references "extended" breastfeeding (as defined by the question as more than 2 years) is the one that shows that a cohort of children tended to be taller if they were not weaned by 3 years of age. In all honesty, the answer seems to contain a lot of incorrect or misleading information.
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BeofettJul 16 '13 at 19:31

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@Ali - you have to be very careful with breastfeeding research. Unfortunately very few organizations and individuals who conduct it are agenda-free. Sometimes you'll find formula companies conducting research trying to show that formula and breastmilk are functionally equivalent (or close). Other times you'll find people who are so taken with breastfeeding that they are willing to stretch and bend and massage the truth. Finding credible sources is unfortunately harder than it should be.
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justktJul 16 '13 at 20:15